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 A223277 Rolling icosahedron face footprints: number of n X 3 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge. 1
 9, 87, 849, 8295, 81057, 792087, 7740273, 75637959, 739134273, 7222821495, 70581425169, 689721818919, 6739962906081, 65862930139863, 643612676665521, 6289384281642375, 61459874978079873, 600586013379170103 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Column 3 of A223282. LINKS R. H. Hardin, Table of n, a(n) for n = 1..210 FORMULA Empirical: a(n) = 11*a(n-1) - 12*a(n-2). Conjectures from Colin Barker, Aug 18 2018: (Start) G.f.: 3*x*(3 - 4*x) / (1 - 11*x + 12*x^2). a(n) = (2^(-1-n)*((11-sqrt(73))^n*(-7+sqrt(73)) + (7+sqrt(73))*(11+sqrt(73))^n)) / sqrt(73). (End) EXAMPLE Some solutions for n=3: ..0..2..3....0..2..3....0..1..4....0..5..9....0..1..6....0..2..0....0..5..9 ..0..2..3....8..2..3....0..1..4....0..5..0....0..1..0....3..2..8....9..5..9 ..0..2..8....0..2..8....0..1..4....0..1..0....4..1..4....3..2..8....0..5..7 Face neighbors: 0 -> 1 2 5 1 -> 0 4 6 2 -> 0 3 8 3 -> 2 4 16 4 -> 3 1 17 5 -> 0 7 9 6 -> 1 7 10 7 -> 6 5 11 8 -> 2 9 13 9 -> 8 5 14 10 -> 6 12 17 11 -> 7 12 14 12 -> 11 10 19 13 -> 8 15 16 14 -> 9 11 15 15 -> 14 13 19 16 -> 3 13 18 17 -> 4 10 18 18 -> 16 17 19 19 -> 15 18 12 CROSSREFS Cf. A223282. Sequence in context: A219123 A144852 A153191 * A267265 A152264 A035101 Adjacent sequences:  A223274 A223275 A223276 * A223278 A223279 A223280 KEYWORD nonn AUTHOR R. H. Hardin, Mar 19 2013 STATUS approved

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Last modified January 19 03:54 EST 2020. Contains 331031 sequences. (Running on oeis4.)